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Gim
b
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s
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Op
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R
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CC B
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.
C
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s
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:
So
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Ham
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a
L
ab
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ato
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C
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p
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Scien
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,
Ar
tific
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I
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tellig
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Secu
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(
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Un
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am
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m
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I
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Gim
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ar
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tr
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d
s
tab
iliz
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[
1
]
,
[
2
]
.
T
h
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tr
ac
k
in
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f
u
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ctio
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en
tails
th
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co
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tin
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je
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[
3
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,
[
4
]
.
T
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p
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p
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f
s
tab
ilizatio
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is
to
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[
5
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[
6
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.
T
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im
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tacle
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im
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am
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ex
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s
[
7
]
.
Ad
v
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co
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tr
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tech
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i
q
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es
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n
ec
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m
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in
v
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lv
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in
th
is
task
[
8
]
.
I
n
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in
em
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[
9
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[
1
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T
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[
1
3
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alg
e
b
r
aic
ap
p
r
o
ac
h
es,
a
n
d
d
is
cu
s
s
ed
th
eir
lim
itatio
n
s
in
ter
m
s
o
f
co
m
p
u
tatio
n
al
ef
f
icien
cy
a
n
d
r
ea
l
-
tim
e
ap
p
li
ca
b
ilit
y
.
T
h
is
c
o
m
p
r
e
h
en
s
iv
e
an
aly
s
is
p
r
o
v
i
d
ed
i
n
s
ig
h
ts
in
t
o
th
e
s
tr
en
g
th
s
a
n
d
wea
k
n
ess
es
o
f
ex
is
tin
g
I
K
s
o
l
u
tio
n
s
,
p
a
v
in
g
th
e
way
f
o
r
th
e
d
ev
elo
p
m
en
t
o
f
m
o
r
e
ef
f
icien
t
alg
o
r
ith
m
s
.
Altan
an
d
Hac
ıo
ğ
lu
[
1
4
]
f
o
cu
s
ed
o
n
th
e
ap
p
licatio
n
o
f
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
MPC
)
f
o
r
a
th
r
ee
-
ax
is
g
im
b
al
s
y
s
tem
m
o
u
n
ted
o
n
u
n
m
a
n
n
e
d
ae
r
ial
v
eh
icles
(
UAVs
)
.
T
h
eir
r
esear
ch
ad
d
r
ess
ed
th
e
ch
a
llen
g
es
o
f
r
ea
l
-
tim
e
tar
g
et
tr
ac
k
in
g
u
n
d
er
ex
ter
n
a
l
d
is
tu
r
b
an
ce
s
,
em
p
h
asizin
g
th
e
n
ee
d
f
o
r
r
o
b
u
s
t
co
n
tr
o
l
a
lg
o
r
ith
m
s
th
at
ca
n
h
an
d
le
d
y
n
am
ic
en
v
ir
o
n
m
en
ta
l
co
n
d
itio
n
s
.
T
h
e
f
in
d
i
n
g
s
f
r
o
m
th
is
s
tu
d
y
ar
e
cr
u
cial
f
o
r
d
e
v
elo
p
in
g
a
d
v
an
ce
d
I
K
alg
o
r
ith
m
s
th
at
en
s
u
r
e
b
o
t
h
ac
cu
r
ac
y
an
d
s
tab
ilit
y
in
g
i
m
b
al
s
y
s
tem
s
.
Gh
af
il
an
d
J
ár
m
ai
[
1
5
]
p
r
esen
te
d
a
d
etailed
ex
p
lo
r
atio
n
o
f
o
p
tim
izatio
n
alg
o
r
ith
m
s
f
o
r
s
o
lv
in
g
in
v
er
s
e
k
in
e
m
atics
p
r
o
b
lem
s
,
ac
co
m
p
an
ied
b
y
MA
T
L
AB
s
o
u
r
ce
co
d
e.
T
h
e
s
tu
d
y
p
r
o
v
i
d
ed
p
r
ac
tical
s
o
lu
tio
n
s
an
d
im
p
lem
en
tatio
n
s
o
f
v
ar
io
u
s
o
p
tim
izatio
n
tech
n
iq
u
es,
h
ig
h
lig
h
tin
g
t
h
eir
ef
f
ec
tiv
en
ess
in
im
p
r
o
v
in
g
I
K
s
o
lu
tio
n
s
.
T
h
is
wo
r
k
s
er
v
es
as
a
v
alu
ab
le
r
eso
u
r
ce
f
o
r
in
teg
r
atin
g
o
p
ti
m
izatio
n
m
eth
o
d
s
in
to
th
e
d
e
v
elo
p
m
en
t
o
f
r
ea
l
-
tim
e
I
K
al
g
o
r
ith
m
s
f
o
r
g
im
b
al
s
y
s
tem
s
.
Similar
ly
,
a
s
tu
d
y
p
r
o
p
o
s
ed
an
o
p
tim
izatio
n
al
g
o
r
ith
m
s
p
ec
if
ically
d
esig
n
e
d
f
o
r
s
o
lv
i
n
g
th
e
I
K
p
r
o
b
lem
o
f
h
u
m
an
u
p
p
er
lim
b
s
in
r
e
h
ab
ilit
atio
n
r
o
b
o
tics
[
1
6
]
.
T
h
eir
a
p
p
r
o
ac
h
,
wh
ich
in
v
o
lv
ed
s
elf
-
a
d
ap
tiv
e
co
n
tr
o
l
p
ar
am
eter
s
in
d
if
f
er
e
n
tial
ev
o
lu
tio
n
(
Pr
o
-
I
SADE
)
,
d
em
o
n
s
tr
ated
s
ig
n
if
ican
t
im
p
r
o
v
em
en
ts
in
s
o
lv
in
g
co
m
p
lex
I
K
p
r
o
b
lem
s
with
h
i
g
h
p
r
ec
is
io
n
.
I
n
th
e
s
am
e
y
ea
r
,
Gh
ae
d
r
a
h
m
ati
an
d
Go
s
s
elin
[
1
7
]
co
n
d
u
cted
a
k
in
em
atic
an
aly
s
is
o
f
a
n
ew
2
-
DOF
p
ar
allel
wr
is
t m
ec
h
an
is
m
with
a
lar
g
e
s
in
g
u
lar
ity
-
f
r
ee
r
o
tatio
n
al.
I
n
d
ee
d
,
t
h
e
p
r
o
ce
s
s
o
f
in
v
er
s
e
k
in
em
atics
in
g
im
b
al
s
y
s
tem
s
in
v
o
lv
es
s
o
lv
in
g
a
s
et
o
f
n
o
n
lin
ea
r
eq
u
atio
n
s
in
o
r
d
e
r
to
ca
lc
u
late
th
e
jo
in
t
c
o
n
f
ig
u
r
atio
n
s
r
eq
u
ir
ed
to
attain
a
s
p
ec
if
ic
e
n
d
-
ef
f
ec
to
r
p
o
s
itio
n
an
d
o
r
ien
tatio
n
[
1
8
]
.
T
h
is
is
s
u
e
is
ex
ac
er
b
ated
b
y
t
h
e
r
e
q
u
ir
em
en
t
f
o
r
in
s
tan
tan
e
o
u
s
p
r
o
ce
s
s
in
g
,
as
t
h
e
s
y
s
tem
m
u
s
t
co
n
s
tan
tly
ad
ap
t
to
ac
cu
r
ately
m
o
n
ito
r
a
m
o
b
ile
t
ar
g
et.
Op
tim
izatio
n
s
tr
ateg
ies
ar
e
ess
en
tial
f
o
r
im
p
r
o
v
in
g
th
e
p
e
r
f
o
r
m
an
ce
o
f
I
K
alg
o
r
ith
m
s
,
r
ed
u
cin
g
co
m
p
u
tatio
n
al
laten
c
y
,
an
d
o
p
tim
izin
g
tr
ac
k
i
n
g
ac
cu
r
ac
y
[
1
9
]
.
T
h
is
s
tu
d
y
f
o
c
u
s
es
o
n
th
e
ad
v
an
ce
m
en
t
an
d
e
n
h
an
ce
m
e
n
t
o
f
in
v
er
s
e
k
i
n
em
atics
alg
o
r
ith
m
s
f
o
r
g
im
b
al
s
y
s
tem
s
,
with
a
s
p
ec
if
ic
em
p
h
asis
o
n
th
eir
u
s
e
in
r
ea
l
-
tim
e
ap
p
licatio
n
s
[
2
0
]
,
[
2
1
]
.
T
h
e
g
o
als ar
e:
a.
Ma
th
em
atica
l
m
o
d
elin
g
in
v
o
l
v
es
cr
ea
tin
g
eq
u
atio
n
s
an
d
t
r
an
s
f
o
r
m
atio
n
s
th
at
ac
cu
r
ately
ca
lcu
late
th
e
p
o
s
itio
n
an
d
o
r
ien
tatio
n
o
f
o
b
jects.
T
h
is
in
v
o
lv
es
th
e
u
tili
za
tio
n
o
f
r
o
tatio
n
m
atr
ices
an
d
tr
an
s
f
o
r
m
atio
n
m
atr
ices to
p
r
ec
is
ely
d
ep
ict
th
e
m
o
tio
n
o
f
th
e
s
y
s
tem
.
b.
Desig
n
in
g
s
o
p
h
is
ticated
I
K
alg
o
r
ith
m
s
th
at
u
s
e
o
p
tim
izatio
n
tech
n
iq
u
es
to
en
h
an
ce
co
m
p
u
tatio
n
al
ef
f
icien
cy
an
d
p
r
ec
is
io
n
.
T
h
e
s
e
alg
o
r
ith
m
s
n
ee
d
to
h
av
e
th
e
ab
ilit
y
to
o
p
er
ate
in
r
ea
l
-
tim
e
in
o
r
d
er
to
g
u
ar
an
tee
u
n
in
ter
r
u
p
ted
a
n
d
a
cc
u
r
ate
tr
ac
k
in
g
o
f
ta
r
g
ets.
c.
T
h
e
cr
ea
ted
al
g
o
r
ith
m
s
will
b
e
in
co
r
p
o
r
ated
i
n
to
a
s
im
u
latio
n
f
r
am
ewo
r
k
u
s
in
g
Simscap
e
Mu
ltib
o
d
y
.
T
h
is
will e
n
ab
le
a
th
o
r
o
u
g
h
ex
am
in
atio
n
an
d
v
is
u
aliza
tio
n
o
f
t
h
e
g
im
b
al
s
y
s
tem
'
s
p
er
f
o
r
m
an
ce
.
T
h
e
p
r
o
p
o
s
ed
s
tu
d
y
f
o
cu
s
es
o
n
en
h
an
cin
g
r
ea
l
-
tim
e
tar
g
et
tr
ac
k
in
g
in
g
im
b
al
s
y
s
tem
s
b
y
in
teg
r
atin
g
th
e
FAB
R
I
K
alg
o
r
ith
m
with
th
e
d
if
f
er
en
tial
ev
o
lu
tio
n
(
DE
)
o
p
tim
izatio
n
tech
n
iq
u
e
[
2
2
]
.
A
co
m
p
ar
ativ
e
an
aly
s
is
h
ig
h
lig
h
ts
th
e
s
ig
n
if
i
ca
n
t
im
p
r
o
v
em
e
n
ts
ac
h
iev
ed
b
y
th
e
FAB
R
I
K
-
DE
m
eth
o
d
,
wh
ich
d
eliv
er
s
th
e
lo
west
m
ea
n
tr
ac
k
in
g
er
r
o
r
(
0
.
0
0
2
m
)
an
d
f
astes
t
co
n
v
e
r
g
en
ce
tim
e
(
2
.
1
2
s
)
c
o
m
p
ar
e
d
t
o
t
r
ad
itio
n
al
m
et
h
o
d
s
(
0
.
0
1
1
m
,
3
.
5
1
s
)
,
g
en
etic
a
lg
o
r
ith
m
(
GA)
(
0
.
0
7
5
m
,
3
.
2
2
s
)
,
an
d
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
(
0
.
0
6
5
m
,
2
.
8
1
s
)
[
2
3
]
,
[
2
4
]
.
T
h
ese
r
esu
lts
em
p
h
asize
th
e
s
u
p
er
io
r
ity
o
f
t
h
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
,
m
a
k
in
g
it
h
ig
h
ly
s
u
itab
le
f
o
r
d
y
n
am
ic
a
n
d
r
ea
l
-
tim
e
ap
p
licatio
n
s
in
m
e
asu
r
em
en
t a
n
d
co
n
tr
o
l sy
s
tem
s
[
2
5
]
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws:
s
ec
tio
n
2
r
ev
iews
r
elate
d
wo
r
k
s
in
th
e
f
ield
,
p
r
o
v
id
in
g
a
b
ac
k
g
r
o
u
n
d
o
n
th
e
ad
v
a
n
ce
m
en
ts
an
d
ch
allen
g
es
in
in
v
er
s
e
k
in
em
atics
an
d
g
im
b
al
s
y
s
tem
o
p
tim
izatio
n
.
Sectio
n
3
d
etails
th
e
b
ac
k
g
r
o
u
n
d
a
n
d
m
eth
o
d
o
lo
g
y
u
s
ed
in
t
h
is
s
tu
d
y
,
i
n
clu
d
in
g
th
e
m
ath
e
m
atica
l
m
o
d
elin
g
,
alg
o
r
ith
m
d
ev
el
o
p
m
en
t,
a
n
d
s
im
u
latio
n
s
etu
p
.
Sectio
n
4
p
r
esen
ts
th
e
r
esu
lts
an
d
d
i
s
cu
s
s
io
n
,
in
clu
d
in
g
s
im
u
latio
n
o
u
tco
m
es,
r
ea
l
-
w
o
r
ld
v
alid
atio
n
,
an
d
co
m
p
a
r
ativ
e
an
aly
s
is
with
ex
is
tin
g
m
eth
o
d
s
.
Fin
ally
,
s
ec
tio
n
5
co
n
clu
d
es th
e
p
a
p
er
an
d
s
u
g
g
ests
d
ir
ec
tio
n
s
f
o
r
f
u
tu
r
e
r
esear
ch
.
2.
T
H
E
P
RO
P
O
SE
D
M
E
T
H
O
D
T
h
is
wo
r
k
aim
s
to
o
p
tim
ize
r
ea
l
-
tim
e
tar
g
et
tr
ac
k
in
g
in
g
i
m
b
al
s
y
s
tem
s
b
y
in
teg
r
atin
g
th
e
FAB
R
I
K
alg
o
r
ith
m
with
th
e
DE
alg
o
r
ith
m
.
T
h
is
co
m
b
in
atio
n
is
e
x
p
ec
ted
t
o
im
p
r
o
v
e
b
o
t
h
th
e
p
er
f
o
r
m
an
ce
an
d
ef
f
icien
cy
o
f
th
e
tr
ac
k
in
g
p
r
o
ce
s
s
.
T
h
is
h
y
b
r
id
ap
p
r
o
ac
h
c
o
m
b
in
es
th
e
ad
v
an
tag
es
o
f
b
o
th
alg
o
r
ith
m
s
:
th
e
s
tr
aig
h
tf
o
r
war
d
n
ess
an
d
co
m
p
u
tin
g
ef
f
ec
tiv
en
ess
o
f
FAB
R
I
K
f
o
r
ad
d
r
ess
in
g
in
v
er
s
e
k
in
e
m
atics
is
s
u
es,
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
5
4
4
-
1
5
5
6
1546
th
e
r
esil
ien
ce
an
d
o
p
tim
izatio
n
s
k
ills
o
f
DE
f
o
r
id
en
tify
in
g
th
e
m
o
s
t
o
p
tim
al
s
o
lu
tio
n
s
in
in
tr
icate
,
m
u
lti
-
d
im
en
s
io
n
al
d
o
m
ain
s
.
T
h
e
m
eth
o
d
co
m
m
en
ce
s
b
y
cr
ea
tin
g
an
elab
o
r
ate
3
D
c
o
m
p
u
ter
-
ai
d
ed
d
esig
n
(
C
AD
)
m
o
d
el
o
f
th
e
g
im
b
al
s
y
s
tem
.
T
h
e
C
AD
m
o
d
el
co
m
p
r
is
es
ess
en
tial
elem
en
ts
,
in
clu
d
in
g
t
h
e
g
im
b
al
b
ase,
y
aw
ass
em
b
ly
,
an
d
p
itch
ass
em
b
ly
.
T
h
e
cr
ea
tio
n
o
f
th
is
m
o
d
el
i
n
v
o
lv
es
th
e
u
tili
za
tio
n
o
f
So
li
d
W
o
r
k
s
,
wh
ich
is
s
u
b
s
eq
u
en
tly
im
p
o
r
ted
in
to
MA
T
L
AB
/S
im
u
lin
k
th
r
o
u
g
h
th
e
Simscap
e
Mu
ltib
o
d
y
p
lu
g
in
.
T
h
e
p
lu
g
i
n
tr
an
s
f
o
r
m
s
C
AD
co
m
p
o
n
e
n
ts
in
to
Simscap
e
Mu
ltib
o
d
y
b
lo
ck
s
,
wh
ile
tr
a
n
s
latin
g
m
o
v
em
en
t
lim
itatio
n
s
in
to
Simscap
e
Mu
ltib
o
d
y
j
o
in
ts
.
T
h
is
en
ab
les
th
e
c
r
ea
tio
n
o
f
a
life
lik
e
s
im
u
latio
n
e
n
v
ir
o
n
m
en
t
f
o
r
th
e
g
im
b
al
s
y
s
tem
.
Fig
u
r
e
1
s
h
o
ws
th
e
3
D
C
AD
m
o
d
el
o
f
th
e
p
r
o
p
o
s
e
d
g
im
b
al
s
y
s
tem
,
in
clu
d
in
g
Fig
u
r
e
1
(
a
)
s
h
o
ws
th
e
g
im
b
al
b
ase
ass
em
b
ly
,
Fig
u
r
e
1
(
b
)
s
h
o
ws
th
e
g
im
b
al
y
aw
ass
em
b
ly
,
an
d
Fig
u
r
e
1
(
c
)
s
h
o
ws
th
e
g
im
b
al
p
itch
ass
em
b
ly
.
(
a)
(
b
)
(
c)
Fig
u
r
e
1
.
3
D
C
AD
m
o
d
el
o
f
t
h
e
p
r
o
p
o
s
ed
g
im
b
al
s
y
s
tem
(
a)
g
im
b
al
b
ase
ass
em
b
ly
,
(
b
)
g
im
b
al
y
aw
ass
em
b
ly
,
an
d
(
c)
g
im
b
al
p
itch
ass
em
b
ly
Af
ter
im
p
o
r
tin
g
th
e
C
AD
m
o
d
el,
th
e
i
n
itializatio
n
p
h
ase
co
n
s
is
t
s
o
f
estab
lis
h
in
g
a
g
r
o
u
p
o
f
p
o
te
n
tial
s
o
lu
tio
n
s
f
o
r
th
e
DE
alg
o
r
ith
m
.
E
v
er
y
m
e
m
b
er
o
f
th
is
p
o
p
u
latio
n
em
b
o
d
ies
a
co
n
ce
iv
ab
l
e
ar
r
an
g
em
e
n
t
o
f
th
e
jo
in
t
an
g
les
in
th
e
g
im
b
al
s
y
s
tem
.
T
h
is
in
itializatio
n
g
u
ar
a
n
tees
a
v
ar
ied
r
a
n
g
e
o
f
in
itial
p
o
s
itio
n
s
,
en
ab
lin
g
th
e
alg
o
r
ith
m
t
o
ef
f
icien
tly
s
ea
r
ch
th
e
s
o
lu
tio
n
s
p
ac
e.
Su
b
s
eq
u
en
tly
,
th
e
FAB
R
I
K
alg
o
r
ith
m
is
im
p
lem
en
ted
o
n
ev
er
y
p
o
ten
tial
s
o
lu
tio
n
in
s
id
e
th
e
p
o
p
u
latio
n
.
T
h
e
FAB
R
I
K
m
eth
o
d
co
n
s
is
ts
o
f
two
p
r
im
ar
y
p
h
ases
:
f
o
r
war
d
r
ea
ch
in
g
an
d
b
ac
k
war
d
r
ea
ch
in
g
.
Du
r
in
g
th
e
f
o
r
war
d
r
ea
ch
in
g
p
h
ase,
th
e
en
d
-
ef
f
ec
to
r
'
s
p
o
s
itio
n
is
ad
ju
s
ted
to
m
atch
th
e
t
ar
g
et
p
o
s
itio
n
,
an
d
ea
ch
jo
in
t
is
s
eq
u
en
tially
ad
ju
s
ted
to
war
d
s
th
e
p
r
ev
io
u
s
jo
in
t
in
th
e
ch
ain
,
s
tar
tin
g
with
th
e
en
d
-
ef
f
ec
to
r
an
d
p
r
o
ce
ed
in
g
to
war
d
s
th
e
b
ase.
T
h
is
m
o
d
if
icatio
n
g
u
ar
an
tees
th
at
th
e
jo
i
n
ts
u
p
h
o
ld
th
e
d
e
s
ig
n
ated
d
is
tan
ce
s
,
th
u
s
k
ee
p
in
g
th
e
k
i
n
em
atic
s
tr
u
ctu
r
e
o
f
th
e
s
y
s
tem
.
Du
r
i
n
g
t
h
e
b
ac
k
war
d
r
ea
ch
i
n
g
p
h
ase,
th
e
p
o
s
itio
n
o
f
th
e
b
ase
jo
in
t
is
r
esto
r
ed
t
o
its
in
i
tial
lo
ca
tio
n
,
an
d
ea
ch
s
u
b
s
eq
u
en
t
jo
in
t
is
s
eq
u
e
n
tially
m
o
v
ed
to
war
d
s
th
e
n
ex
t
jo
in
t
in
th
e
ch
ain
,
s
tar
tin
g
at
th
e
b
ase
an
d
en
d
in
g
at
th
e
en
d
-
ef
f
ec
to
r
.
T
h
e
p
r
o
ce
s
s
is
iter
ated
u
n
til
th
e
en
d
-
ef
f
ec
to
r
r
ea
ch
es
a
tar
g
et
p
o
in
t
th
at
is
s
u
itab
ly
clo
s
e,
with
in
a
s
et
to
ler
an
ce
.
Af
ter
th
e
FAB
R
I
K
alg
o
r
ith
m
h
as
p
r
o
d
u
ce
d
an
a
p
p
r
o
x
im
ate
s
o
lu
tio
n
f
o
r
t
h
e
d
esire
d
jo
in
t
p
o
s
itio
n
s
,
th
e
DE
m
eth
o
d
is
u
s
ed
to
en
h
an
ce
a
n
d
im
p
r
o
v
e
t
h
ese
co
n
f
ig
u
r
atio
n
s
.
T
h
e
DE
alg
o
r
ith
m
f
u
n
ctio
n
s
b
y
ex
ec
u
tin
g
th
r
ee
p
r
im
a
r
y
s
tep
s
:
m
u
tatio
n
,
cr
o
s
s
o
v
er
,
an
d
s
elec
tio
n
.
D
u
r
in
g
th
e
m
u
tatio
n
s
tep
,
a
m
u
ta
n
t
v
ec
to
r
is
cr
ea
ted
b
y
co
m
b
i
n
in
g
th
e
weig
h
ted
d
if
f
er
en
ce
o
f
two
r
an
d
o
m
ly
c
h
o
s
en
p
o
p
u
latio
n
v
ec
t
o
r
s
with
a
th
ir
d
v
ec
to
r
.
T
h
e
cr
o
s
s
o
v
er
s
tag
e
in
v
o
lv
es
th
e
cr
ea
tio
n
o
f
a
t
r
ial
v
ec
to
r
b
y
m
er
g
in
g
th
e
m
u
tan
t
v
ec
t
o
r
an
d
t
h
e
tar
g
et
v
ec
to
r
.
Du
r
in
g
th
e
s
e
lectio
n
p
r
o
ce
s
s
,
th
e
tr
ial
v
ec
to
r
is
ass
es
s
ed
ag
ain
s
t
th
e
tar
g
et
v
ec
to
r
u
s
in
g
a
n
o
b
jectiv
e
f
u
n
ctio
n
.
I
f
th
e
tr
ial
v
ec
to
r
p
r
o
d
u
ce
s
a
s
u
p
er
io
r
v
al
u
e
f
o
r
th
e
g
o
al
f
u
n
ctio
n
,
it
will
r
ep
lace
th
e
tar
g
et
v
ec
to
r
i
n
th
e
p
o
p
u
latio
n
f
o
r
th
e
s
u
b
s
eq
u
en
t
g
en
er
atio
n
.
T
h
e
in
teg
r
ate
d
al
g
o
r
ith
m
s
eq
u
en
tially
e
x
ec
u
te
s
th
e
FAB
R
I
K
an
d
DE
p
r
o
ce
d
u
r
es
f
o
r
a
p
r
e
-
estab
lis
h
ed
n
u
m
b
e
r
o
f
iter
ati
o
n
s
o
r
u
n
til
a
co
n
v
er
g
e
n
ce
r
eq
u
ir
em
e
n
t
is
s
atis
f
ied
,
s
u
c
h
as
a
s
ig
n
if
ica
n
t
r
ed
u
ctio
n
in
th
e
o
b
jectiv
e
f
u
n
ctio
n
ac
r
o
s
s
co
n
s
ec
u
tiv
e
iter
atio
n
s
.
T
h
e
iter
ativ
e
tech
n
iq
u
e
g
u
ar
an
tees
th
at
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Mo
d
elin
g
a
n
d
en
h
a
n
ci
n
g
in
ve
r
s
e
kin
ema
tics
a
lg
o
r
ith
ms fo
r
r
ea
l
-
time
ta
r
g
et
…
(
A
b
d
era
h
m
a
n
K
r
io
u
ile
)
1547
g
im
b
al
s
y
s
tem
m
ay
r
ea
c
h
r
ea
l
-
tim
e
p
er
f
o
r
m
an
ce
w
h
ile
also
m
ain
tain
in
g
ex
ce
llen
t
p
r
ec
i
s
io
n
an
d
r
o
b
u
s
tn
ess
ag
ain
s
t e
x
ter
n
al
d
is
tu
r
b
a
n
ce
s
.
T
h
e
co
m
b
in
atio
n
o
f
t
h
e
FAB
R
I
K
alg
o
r
ith
m
'
s
ef
f
ec
tiv
en
ess
in
h
an
d
lin
g
in
v
er
s
e
k
in
e
m
atics
p
r
o
b
lem
s
an
d
th
e
DE
alg
o
r
ith
m
'
s
o
p
tim
izatio
n
ca
p
ab
ilit
ies
r
esu
lts
in
a
r
o
b
u
s
t
s
o
lu
tio
n
f
o
r
r
ea
l
-
tim
e
tar
g
et
tr
ac
k
in
g
i
n
g
im
b
al
s
y
s
tem
s
.
T
h
is
tech
n
o
l
o
g
y
g
u
ar
an
tees
m
eticu
lo
u
s
m
an
ag
em
en
t
o
f
th
e
g
im
b
al'
s
o
r
ien
tatio
n
,
allo
win
g
it
to
ad
ju
s
t
to
d
y
n
am
ic
v
ar
iatio
n
s
in
th
e
s
u
r
r
o
u
n
d
i
n
g
s
an
d
c
o
r
r
ec
tly
f
o
llo
w
m
o
v
in
g
s
u
b
je
cts.
As
s
h
o
wn
in
Alg
o
r
ith
m
1
,
th
e
co
m
b
in
ed
F
AB
R
I
K
an
d
DE
alg
o
r
ith
m
in
teg
r
ates
th
e
s
tr
en
g
th
s
o
f
b
o
th
m
eth
o
d
s
to
o
p
tim
ize
r
ea
l
-
tim
e
tar
g
et
tr
ac
k
in
g
in
g
im
b
al
s
y
s
tem
s
.
Alg
o
r
ith
m
1
.
C
o
m
b
in
ed
F
AB
R
I
K
an
d
d
if
f
er
en
tial e
v
o
lu
tio
n
(
DE
)
alg
o
r
it
h
m
Procedure FABRIK_DE (
P,
T,
,
,
,
,
_
)
−
Input:
o
Chain of joints
=
{
1
,
2
,
…
,
}
o
Target position
T
o
Tolerance
o
Population
X
o
Mutation factor
F
o
Crossover rate
o
Maximum generations max_gen
−
Output: Optimized joint positions
P
1.
For each candidate solution
:
o
Apply FABRIK to xix_i:
▪
Repeat:
▪
Forward Reaching:
=
+
1
+
‖
+
1
−
‖
(
−
+
1
)
▪
Backward Reaching:
+
1
=
+
‖
+
1
−
‖
(
+
1
−
)
▪
Until
‖
−
‖
≤
.
2.
For gen=1 to max_gen:
o
For each target vector
in the population
X
:
▪
Mutation:
←
+
.
(
2
−
3
)
▪
Crossover:
←
{
,
(
0
,
1
)
≤
=
,
ℎ
▪
Selection:
If
(
)
≤
(
)
,
ℎ
←
.
3.
End For
4.
End Procedure
3.
RE
S
E
ARCH
M
E
T
H
O
D
3
.
1
.
G
im
ba
l
o
v
er
v
iew
Gim
b
als
ar
e
d
ev
ices
th
at
ca
n
r
o
tate
ar
o
u
n
d
t
h
eir
ax
es
to
p
o
s
itio
n
an
attac
h
e
d
item
.
T
h
ey
ca
n
b
e
s
p
h
er
ical
o
r
cy
lin
d
r
ical
an
d
a
r
e
m
o
u
n
ted
o
n
a
b
ase.
T
h
e
g
im
b
al
p
er
f
o
r
m
s
t
h
r
ee
m
ain
f
u
n
ctio
n
s
:
tar
g
etin
g
,
wh
ich
en
tails
th
e
p
r
ec
is
e
co
n
t
r
o
l
o
f
th
e
g
im
b
al'
s
aim
eith
er
m
an
u
ally
o
r
au
to
m
atica
lly
;
s
tab
ilizatio
n
,
wh
ich
co
u
n
ter
ac
ts
an
y
u
n
in
ten
d
e
d
m
o
v
em
en
ts
o
f
th
e
b
ase
to
m
ain
tain
th
e
o
b
ject'
s
s
tab
ilit
y
;
an
d
tr
ac
k
in
g
[
2
6
]
.
Gim
b
als
h
av
e
ex
te
n
s
iv
e
u
s
es
in
s
ev
er
al
f
ield
s
lik
e
as
ast
r
o
n
o
m
y
,
telec
o
m
m
u
n
icatio
n
s
,
an
d
m
ilit
ar
y
an
d
s
ec
u
r
ity
.
T
h
ey
ar
e
u
tili
ze
d
f
o
r
th
e
p
u
r
p
o
s
e
o
f
m
o
v
in
g
telesco
p
es,
s
tab
ilizin
g
ca
m
er
as,
an
d
m
o
n
ito
r
in
g
m
o
v
in
g
o
b
jects.
Gim
b
als
ar
e
v
ital
f
o
r
im
p
r
o
v
in
g
th
e
f
u
n
cti
o
n
in
g
o
f
m
an
y
ad
v
an
ce
d
tech
n
o
lo
g
ical
s
y
s
tem
s
b
ec
au
s
e
to
th
eir
v
ar
iety
an
d
p
r
ec
is
io
n
[
2
7
]
.
Fig
u
r
e
2
(
a)
s
h
o
ws
a
g
im
b
al
f
o
r
telesco
p
e
s
tab
ilizatio
n
in
o
b
s
er
v
ato
r
ies
an
d
Fig
u
r
e
2
(
b
)
p
r
esen
ts
a
g
im
b
al
-
m
o
u
n
ted
ca
m
er
a
s
y
s
tem
f
o
r
ae
r
ial
s
u
r
v
eillan
ce
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
5
4
4
-
1
5
5
6
1548
I
n
d
ee
d
,
th
e
p
o
s
itio
n
o
f
a
p
o
in
t
in
s
p
ac
e
is
d
ef
in
e
d
b
y
its
co
o
r
d
in
ates,
wh
ich
r
ep
r
esen
t
t
h
e
d
is
tan
ce
s
f
r
o
m
t
h
e
o
r
i
g
in
alo
n
g
ea
c
h
ax
is
in
a
co
o
r
d
in
ate
s
y
s
tem
(
f
o
r
ex
am
p
le,
{
2
3
5
}
T
in
an
XYZ
s
y
s
tem
)
.
I
n
o
r
d
e
r
to
ch
ar
ac
ter
ize
a
p
o
in
t
in
r
elat
io
n
to
an
o
t
h
er
p
o
in
t
in
s
tead
o
f
th
e
o
r
ig
in
,
a
n
ew
co
o
r
d
in
ate
s
y
s
tem
,
also
k
n
o
wn
as
a
r
ef
er
en
ce
f
r
a
m
e,
is
in
tr
o
d
u
ce
d
.
T
h
is
n
ew
f
r
am
e
u
tili
ze
s
an
alter
n
ativ
e
p
o
in
t
as
its
r
ef
er
en
ce
,
en
a
b
lin
g
th
e
p
o
s
s
ib
ilit
y
o
f
p
o
s
itio
n
in
g
in
r
elatio
n
to
it.
C
o
o
r
d
in
ate
tr
an
s
f
o
r
m
atio
n
s
ar
e
u
s
ed
to
co
n
v
e
r
t
co
o
r
d
in
ates
f
r
o
m
o
n
e
r
e
f
er
en
ce
f
r
am
e
to
an
o
t
h
er
.
T
h
ese
t
r
an
s
f
o
r
m
atio
n
s
ca
n
in
v
o
l
v
e
p
u
r
e
t
r
an
s
latio
n
,
p
u
r
e
r
o
tatio
n
,
o
r
b
o
th
.
T
r
an
s
latio
n
in
its
p
u
r
e
f
o
r
m
in
v
o
lv
es
s
h
if
tin
g
th
e
r
ef
er
en
c
e
p
o
in
t
o
f
o
n
e
co
o
r
d
in
ate
s
y
s
tem
to
an
o
th
e
r
b
y
in
co
r
p
o
r
atin
g
a
v
ec
to
r
th
at
r
e
p
r
esen
ts
th
e
d
is
p
lace
m
en
t.
Pu
r
e
r
o
tatio
n
r
ef
er
s
to
t
h
e
p
r
o
ce
s
s
o
f
alig
n
in
g
o
n
e
f
r
am
e
with
an
o
t
h
er
b
y
u
tili
zin
g
a
tr
an
s
f
o
r
m
atio
n
m
at
r
ix
[
2
8
]
.
A
two
-
d
eg
r
ee
-
of
-
f
r
ee
d
o
m
(
2
-
DOF)
g
im
b
a
l
s
y
s
tem
u
tili
ze
s
m
u
ltip
le
r
ef
er
en
ce
f
r
a
m
es
to
ac
c
u
r
ately
d
escr
ib
e
an
d
an
al
y
ze
th
e
m
o
v
em
en
ts
o
f
t
h
e
g
im
b
al
an
d
its
co
m
p
o
n
e
n
ts
[
2
9
]
.
E
ac
h
r
ef
er
en
ce
f
r
am
e
s
er
v
es
a
s
p
ec
if
ic
r
o
le
in
ca
p
tu
r
i
n
g
th
e
d
y
n
am
ics
an
d
k
in
em
atics o
f
th
e
s
y
s
tem
[
3
0
]
.
(
a)
(
b
)
Fig
u
r
e
2
.
Use c
ases
o
f
g
im
b
als (
a)
g
im
b
al
f
o
r
telesco
p
e
s
tab
ilizatio
n
in
o
b
s
er
v
ato
r
ies an
d
(
b
)
g
im
b
al
-
m
o
u
n
ted
ca
m
e
r
a
s
y
s
tem
f
o
r
ae
r
ial
s
u
r
v
eillan
ce
3
.
2
.
Dy
na
m
ic
equa
t
io
ns
o
f
g
i
m
ba
l
T
h
e
d
y
n
am
ic
e
q
u
atio
n
s
a
r
e
e
s
s
en
tial
f
o
r
ca
p
tu
r
i
n
g
t
h
e
m
e
ch
an
ical
b
eh
a
v
io
r
o
f
g
im
b
al
s
y
s
tem
s
.
I
n
class
ical
m
ec
h
an
ics,
th
e
Ne
wto
n
–
E
u
ler
eq
u
atio
n
s
d
escr
i
b
e
th
e
co
m
b
i
n
ed
tr
an
s
latio
n
al
an
d
r
o
tatio
n
al
d
y
n
am
ics
o
f
a
r
ig
id
b
o
d
y
.
T
h
e
s
e
eq
u
atio
n
s
r
elate
th
e
m
o
tio
n
o
f
th
e
ce
n
ter
o
f
m
ass
o
f
a
r
i
g
id
b
o
d
y
to
th
e
s
u
m
o
f
f
o
r
ce
s
an
d
to
r
q
u
es (
o
r
m
o
m
en
ts
)
ac
tin
g
u
p
o
n
it
[
3
1
]
.
Sin
ce
th
e
m
o
v
em
e
n
ts
o
f
g
im
b
als a
r
e
p
u
r
ely
r
o
tatio
n
al,
lin
ea
r
f
o
r
ce
s
ap
p
lied
to
th
e
ce
n
ter
o
f
th
e
r
o
tatio
n
al
ax
es
o
f
th
e
in
n
er
an
d
o
u
ter
g
im
b
als
d
o
n
o
t
cr
ea
te
an
y
n
et
to
r
q
u
e
[
3
2
]
.
T
h
er
ef
o
r
e,
o
n
ly
E
u
ler
’
s
eq
u
atio
n
s
,
wh
ich
r
ep
r
esen
t
r
o
tatio
n
al
m
o
tio
n
s
,
ar
e
ex
am
in
ed
to
o
b
tai
n
a
m
ath
em
atica
l m
o
d
el
o
f
th
e
g
i
m
b
al
s
y
s
tem
.
E
u
ler
’
s
eq
u
atio
n
s
f
o
r
r
o
tatio
n
al
d
y
n
a
m
ics s
tate
th
at
th
e
to
tal
to
r
q
u
e
ac
tin
g
ab
o
u
t
th
e
ce
n
ter
o
f
m
as
s
is
eq
u
al
to
th
e
p
r
o
d
u
ct
o
f
th
e
m
o
m
en
t
o
f
in
er
tia
a
b
o
u
t
th
e
ce
n
ter
o
f
m
ass
an
d
th
e
an
g
u
lar
ac
ce
ler
atio
n
,
p
lu
s
th
e
cr
o
s
s
p
r
o
d
u
ct
o
f
th
e
a
n
g
u
lar
v
elo
city
an
d
th
e
p
r
o
d
u
ct
o
f
an
g
u
la
r
v
elo
city
an
d
m
o
m
en
t o
f
in
er
tia.
Ma
th
e
m
atica
lly
,
E
u
ler
’
s
eq
u
atio
n
s
ar
e
ex
p
r
ess
ed
as
(
1
)
:
=
⋅
+
×
(
⋅
)
(
1
)
wer
e,
is
t
h
e
t
o
r
q
u
e
v
ec
t
o
r
a
cti
n
g
o
n
t
h
e
b
o
d
y
;
is
t
h
e
m
o
m
en
t
o
f
i
n
e
r
ti
a
te
n
s
o
r
;
is
t
h
e
a
n
g
u
lar
ac
ce
l
er
ati
o
n
v
e
ct
o
r
;
an
d
is
t
h
e
a
n
g
u
la
r
v
el
o
cit
y
v
e
ct
o
r
.
T
h
ese
eq
u
atio
n
s
ar
e
cr
u
cial
f
o
r
c
o
m
p
r
e
h
en
d
i
n
g
an
d
f
o
r
ec
a
s
tin
g
th
e
b
eh
av
i
o
r
o
f
th
e
g
im
b
al
s
y
s
tem
u
n
d
er
d
if
f
er
e
n
t
cir
cu
m
s
tan
ce
s
.
B
y
u
tili
zin
g
E
u
ler
'
s
eq
u
atio
n
s
,
o
n
e
ca
n
p
r
o
p
er
ly
s
im
u
late
th
e
r
o
tatio
n
al
d
y
n
am
ics
o
f
th
e
g
im
b
al.
T
h
is
en
ab
les
th
e
d
e
v
elo
p
m
e
n
t
o
f
co
n
tr
o
l
tec
h
n
iq
u
es
th
at
e
n
s
u
r
e
s
tab
ilit
y
an
d
p
r
ec
is
io
n
in
tr
ac
k
i
n
g
tar
g
ets.
3
.
3
.
O
ptim
iza
t
io
n o
f
I
K
a
lg
o
ri
t
hm
s
f
o
r
g
i
m
ba
l sy
s
t
em
s
T
h
e
o
p
tim
izatio
n
o
f
I
K
alg
o
r
ith
m
s
f
o
r
r
ea
l
-
tim
e
tar
g
et
tr
ac
k
in
g
in
g
im
b
al
s
y
s
tem
s
in
v
o
lv
es
en
h
an
cin
g
co
m
p
u
tatio
n
al
ef
f
i
cien
cy
an
d
ac
cu
r
ac
y
to
e
n
s
u
r
e
p
r
ec
is
e
a
n
d
s
tab
le
t
r
ac
k
in
g
u
n
d
er
d
y
n
am
ic
co
n
d
itio
n
s
.
T
h
is
p
r
o
ce
s
s
in
co
r
p
o
r
ates
ad
v
an
ce
d
tech
n
iq
u
es
an
d
m
ath
em
atica
l
f
o
r
m
u
latio
n
s
to
a
d
d
r
ess
th
e
co
m
p
lex
ities
o
f
r
ea
l
-
tim
e
ap
p
licatio
n
s
[
3
3
]
.
T
h
ese
co
m
p
l
ex
ities
ar
is
e
f
r
o
m
th
e
n
ee
d
to
p
r
o
ce
s
s
r
ap
id
ly
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Mo
d
elin
g
a
n
d
en
h
a
n
ci
n
g
in
ve
r
s
e
kin
ema
tics
a
lg
o
r
ith
ms fo
r
r
ea
l
-
time
ta
r
g
et
…
(
A
b
d
era
h
m
a
n
K
r
io
u
ile
)
1549
ch
an
g
in
g
in
p
u
t
d
ata,
s
u
ch
as
t
ar
g
et
m
o
v
em
en
ts
an
d
p
latf
o
r
m
d
is
tu
r
b
an
ce
s
,
with
in
tig
h
t
ti
m
e
co
n
s
tr
ain
ts
.
T
h
e
alg
o
r
ith
m
s
m
u
s
t
also
ad
ap
t
t
o
v
ar
y
in
g
en
v
i
r
o
n
m
e
n
tal
co
n
d
itio
n
s
,
s
u
ch
as
s
u
d
d
en
ac
ce
l
er
atio
n
s
o
r
ex
ter
n
al
f
o
r
ce
s
,
wh
ich
ca
n
s
ig
n
if
ican
tl
y
im
p
ac
t
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
.
T
o
ac
h
ie
v
e
th
ese
g
o
als,
th
e
s
tu
d
y
in
te
g
r
ates
o
p
tim
izatio
n
s
tr
ateg
ies
lik
e
co
n
s
tr
ain
t
h
an
d
lin
g
,
g
r
a
d
ien
t
-
b
as
ed
m
eth
o
d
s
,
an
d
m
ac
h
in
e
lear
n
in
g
tec
h
n
iq
u
es
to
f
in
e
-
tu
n
e
t
h
e
alg
o
r
ith
m
s
f
o
r
b
o
th
s
p
ee
d
an
d
p
r
ec
is
io
n
.
3
.
3
.
1
.
F
o
rwa
rd
a
nd
ba
ck
w
a
r
d r
ea
ching
inv
er
s
e
k
inem
a
t
i
cs
(
F
AB
RIK)
FAB
R
I
K
is
an
iter
ativ
e
I
K
alg
o
r
ith
m
d
esig
n
ed
f
o
r
co
m
p
u
tatio
n
al
ef
f
icien
cy
an
d
r
ea
l
-
tim
e
ap
p
licatio
n
s
[
3
4
]
.
I
t
alter
n
ates
b
etwe
en
f
o
r
war
d
a
n
d
b
ac
k
wa
r
d
p
ass
es
th
r
o
u
g
h
th
e
k
in
em
at
ic
ch
ain
,
ad
j
u
s
tin
g
jo
in
t
an
g
les
to
m
in
im
ize
th
e
d
is
tan
ce
b
etwe
en
th
e
en
d
-
ef
f
ec
t
o
r
an
d
th
e
tar
g
et
p
o
s
itio
n
.
Giv
en
a
ch
ain
o
f
jo
in
ts
=
{
1
,
2
,
…
,
}
with
th
e
tar
g
et
p
o
s
itio
n
.
I
n
t
h
e
f
o
r
war
d
r
ea
ch
in
g
p
h
ase,
th
e
p
r
im
ar
y
o
b
jectiv
e
is
to
s
et
th
e
p
o
s
itio
n
o
f
th
e
en
d
-
ef
f
ec
to
r
to
th
e
tar
g
et
p
o
s
itio
n
.
T
h
is
is
d
o
n
e
b
y
in
itially
ass
ig
n
in
g
t
h
e
en
d
-
ef
f
ec
to
r
to
th
e
tar
g
et
p
o
s
itio
n
.
On
ce
th
e
en
d
-
e
f
f
ec
to
r
is
alig
n
ed
with
t
h
e
tar
g
et,
th
e
al
g
o
r
ith
m
th
en
p
r
o
ce
ed
s
to
m
o
v
e
ea
ch
jo
in
t
t
o
war
d
s
th
e
p
r
ev
i
o
u
s
jo
in
t
in
t
h
e
ch
ai
n
,
s
tar
tin
g
f
r
o
m
th
e
e
n
d
-
e
f
f
ec
to
r
an
d
m
o
v
in
g
to
war
d
s
th
e
b
ase.
Ma
th
em
atica
lly
,
th
is
ad
j
u
s
tm
en
t is p
er
f
o
r
m
e
d
u
s
in
g
(
2
)
:
=
+
1
+
‖
+
1
−
‖
(
−
+
1
)
(
2
)
wh
er
e
r
ep
r
esen
ts
th
e
d
is
tan
c
e
b
etwe
en
jo
in
t
an
d
jo
in
t
+1
.
T
h
is
en
s
u
r
es
th
at
th
e
n
ew
p
o
s
itio
n
o
f
ea
ch
jo
in
t
is
co
r
r
ec
tly
ca
lcu
lated
to
m
ain
tain
th
e
s
p
ec
if
ied
d
is
tan
ce
s
,
th
er
eb
y
p
r
eser
v
in
g
th
e
k
in
em
atic
s
tr
u
ctu
r
e
o
f
th
e
s
y
s
tem
.
I
n
t
h
e
b
ac
k
war
d
r
ea
c
h
in
g
p
h
ase,
th
e
al
g
o
r
ith
m
f
o
c
u
s
es
o
n
r
e
-
estab
lis
h
in
g
th
e
p
o
s
itio
n
o
f
th
e
b
ase
jo
in
t
to
its
o
r
i
g
in
al
lo
ca
ti
o
n
.
T
h
is
s
tep
is
cr
itical
as
it
en
s
u
r
es
th
at
th
e
r
o
o
t
o
f
th
e
k
in
e
m
atic
ch
ain
r
em
ain
s
f
ix
ed
,
p
r
o
v
id
in
g
a
s
tab
le
f
o
u
n
d
atio
n
f
o
r
th
e
s
y
s
tem
.
T
h
e
p
o
s
itio
n
o
f
th
e
b
ase
jo
in
t
1
is
s
et
b
ac
k
to
its
o
r
ig
in
al
p
o
s
itio
n
.
Fo
llo
win
g
th
is
,
th
e
alg
o
r
ith
m
iter
ates
f
r
o
m
th
e
b
a
s
e
to
war
d
s
th
e
en
d
-
ef
f
ec
to
r
,
a
d
ju
s
tin
g
ea
ch
s
u
b
s
eq
u
en
t jo
in
t
+
1
u
s
in
g
(
3
)
.
+
1
=
+
‖
+
1
−
‖
(
+
1
−
)
(
3
)
T
h
is
s
tep
en
s
u
r
es
th
at
th
e
jo
i
n
ts
ar
e
m
o
v
e
d
to
war
d
s
th
e
n
e
x
t
jo
in
t
in
t
h
e
ch
ain
,
th
u
s
p
r
e
s
er
v
in
g
th
e
o
v
er
all
s
tr
u
ctu
r
e
an
d
alig
n
m
e
n
t
o
f
th
e
s
y
s
tem
.
As
s
h
o
wn
in
Alg
o
r
ith
m
2
,
th
e
FAB
R
I
K
alg
o
r
ith
m
iter
ativ
ely
ad
ju
s
ts
th
e
jo
in
t p
o
s
itio
n
s
u
n
til th
e
en
d
-
ef
f
ec
to
r
is
s
u
f
f
icien
tly
clo
s
e
to
th
e
tar
g
et
p
o
s
itio
n
.
Alg
o
r
ith
m
2
.
T
h
e
FAB
R
I
K
alg
o
r
ith
m
Procedure FABRIK(
P,
T,
)
−
Input:
o
Chain of joints
=
{
1
,
2
,
…
,
}
o
Target position
T
o
Tolerance
−
Output:
Updated
joint positions
P
1.
←
2.
Repeat:
o
Forward Reaching:
▪
For
i = n
–
1 to 1:
=
+
1
+
‖
+
1
−
‖
(
−
+
1
)
o
Backward Reaching:
1
←
// Set the base joint to its original position.
▪
For I = 1 to n
-
1:
+
1
=
+
‖
+
1
−
‖
(
+
1
−
)
3.
Until
‖
−
‖
≤
.
4.
End Procedure
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
5
4
4
-
1
5
5
6
1550
T
h
is
p
r
o
ce
s
s
in
v
o
lv
es
alter
n
at
in
g
b
etwe
en
f
o
r
war
d
an
d
b
ac
k
war
d
r
ea
ch
i
n
g
s
tep
s
,
wh
ich
ef
f
icien
tly
m
in
im
ize
th
e
d
is
tan
ce
b
etwe
en
th
e
jo
i
n
ts
an
d
en
s
u
r
e
t
h
e
d
esire
d
co
n
f
ig
u
r
atio
n
is
ac
h
iev
ed
.
T
h
e
f
o
r
war
d
r
ea
ch
in
g
p
h
ase
s
ets
th
e
e
n
d
-
e
f
f
ec
to
r
t
o
th
e
tar
g
et
p
o
s
itio
n
an
d
m
o
v
es
ea
ch
jo
in
t
t
o
war
d
s
th
e
p
r
e
v
io
u
s
o
n
e,
wh
ile
th
e
b
ac
k
war
d
r
ea
ch
i
n
g
p
h
ase
r
e
-
estab
lis
h
es
th
e
b
ase
jo
in
t'
s
p
o
s
itio
n
an
d
m
o
v
es
ea
ch
s
u
b
s
eq
u
en
t
jo
in
t
to
war
d
s
th
e
n
ex
t
o
n
e.
B
y
r
e
p
e
atin
g
th
ese
s
tep
s
,
th
e
FAB
R
I
K
alg
o
r
ith
m
p
r
o
v
id
es
a
co
m
p
u
tatio
n
ally
ef
f
icien
t
an
d
r
o
b
u
s
t so
lu
tio
n
f
o
r
r
ea
l
-
tim
e
tar
g
et
tr
ac
k
in
g
in
g
im
b
al
s
y
s
tem
s
[
3
5
]
.
3
.
3
.
2
.
Dif
f
er
ent
ia
l
ev
o
lutio
n a
lg
o
rit
hm
T
h
e
d
if
f
er
en
tial
ev
o
l
u
tio
n
(
DE
)
alg
o
r
ith
m
is
a
p
o
p
u
latio
n
-
b
a
s
ed
o
p
tim
izatio
n
m
eth
o
d
th
at
iter
ativ
ely
im
p
r
o
v
es
ca
n
d
id
ate
s
o
lu
tio
n
s
with
r
esp
ec
t
to
a
g
iv
en
m
ea
s
u
r
e
o
f
q
u
ality
o
r
f
itn
ess
.
D
if
f
er
en
tial
ev
o
lu
tio
n
is
p
ar
ticu
lar
ly
well
-
s
u
ited
f
o
r
co
n
tin
u
o
u
s
o
p
tim
izatio
n
p
r
o
b
le
m
s
,
m
ak
in
g
it id
ea
l f
o
r
ap
p
licatio
n
s
s
u
ch
as in
v
er
s
e
k
in
em
atics
in
g
im
b
al
s
y
s
tem
s
wh
er
e
p
r
ec
is
io
n
an
d
ad
ap
ta
b
ilit
y
ar
e
cr
u
cial
[
3
6
]
.
T
h
e
m
e
th
o
d
lev
er
a
g
es
th
e
d
if
f
er
en
ce
s
b
etwe
en
r
an
d
o
m
ly
s
elec
ted
p
air
s
o
f
s
o
l
u
tio
n
s
to
d
r
iv
e
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
,
en
s
u
r
in
g
a
r
o
b
u
s
t
b
alan
ce
b
etwe
en
e
x
p
lo
r
atio
n
a
n
d
ex
p
lo
itatio
n
o
f
th
e
s
o
lu
tio
n
s
p
ac
e
[
3
7
]
.
T
h
e
d
if
f
e
r
en
tial
e
v
o
lu
tio
n
al
g
o
r
ith
m
is
p
ar
ticu
lar
ly
ef
f
ec
tiv
e
f
o
r
r
ea
l
-
tim
e
tar
g
et
tr
ac
k
in
g
in
g
im
b
al
s
y
s
tem
s
d
u
e
to
it
s
ab
ilit
y
to
f
in
d
g
lo
b
al
o
p
tim
a
in
co
m
p
lex
,
m
u
lti
-
d
im
en
s
io
n
al
lan
d
s
ca
p
es
[
3
8
]
.
As
d
etai
led
in
Alg
o
r
ith
m
3
,
th
e
d
if
f
er
en
tial
ev
o
lu
tio
n
alg
o
r
ith
m
iter
ativ
ely
en
h
a
n
ce
s
ca
n
d
id
ate
s
o
lu
tio
n
s
b
y
u
tili
zin
g
th
e
d
if
f
er
e
n
ce
s
b
etwe
en
r
an
d
o
m
ly
s
elec
ted
p
air
s
o
f
s
o
lu
tio
n
s
.
Alg
o
r
ith
m
3
.
T
h
e
d
if
f
er
en
tial
ev
o
lu
tio
n
(
DE
)
alg
o
r
ith
m
Procedure DE (
X,
F
,
)
−
Input:
o
Population of candidate solutions
X
o
Mutation factor
F
o
Crossover rate
−
Output:
Optimized solution
1.
For each target vector
in the population
X
:
o
Mutation:
←
1
+
.
(
2
−
3
)
o
Crossover:
←
{
,
(
0
,
1
)
≤
=
,
ℎ
o
Selection:
If
(
)
≤
(
)
,
ℎ
←
.
2.
End For
3.
End Procedure
T
h
e
DE
alg
o
r
ith
m
f
o
llo
ws
a
th
r
ee
-
s
tep
p
r
o
ce
s
s
:
m
u
tatio
n
,
cr
o
s
s
o
v
er
,
an
d
s
elec
tio
n
.
D
u
r
in
g
t
h
e
m
u
tatio
n
p
h
ase,
a
m
u
tan
t
v
e
cto
r
is
g
en
er
ated
b
y
ad
d
in
g
th
e
weig
h
ted
d
if
f
er
en
ce
b
etwe
en
two
r
an
d
o
m
ly
s
elec
ted
p
o
p
u
latio
n
v
ec
to
r
s
to
a
th
ir
d
v
ec
to
r
.
T
h
is
is
f
o
llo
wed
b
y
th
e
cr
o
s
s
o
v
er
p
h
ase,
wh
er
e
a
tr
ial
v
ec
to
r
is
cr
ea
ted
b
y
c
o
m
b
in
i
n
g
th
e
m
u
t
an
t
v
ec
to
r
a
n
d
th
e
tar
g
et
v
ec
to
r
.
Fin
ally
,
th
e
s
elec
tio
n
p
h
ase
d
eter
m
in
es
wh
eth
e
r
th
e
tr
ial
v
ec
t
o
r
o
r
t
h
e
tar
g
et
v
ec
to
r
will
a
d
v
an
ce
to
t
h
e
n
ex
t
g
en
e
r
atio
n
b
ased
o
n
th
eir
r
esp
ec
tiv
e
f
itn
ess
v
alu
es.
B
y
co
n
tin
u
o
u
s
ly
a
p
p
ly
in
g
t
h
ese
s
tep
s
,
th
e
DE
alg
o
r
ith
m
ef
f
icien
tly
b
alan
ce
s
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
o
f
th
e
s
o
lu
tio
n
s
p
ac
e,
m
ak
in
g
it
a
r
o
b
u
s
t
o
p
ti
m
izatio
n
tech
n
iq
u
e
f
o
r
s
o
l
v
in
g
co
m
p
lex
i
n
v
er
s
e
k
in
em
atics p
r
o
b
lem
s
in
r
ea
l
-
ti
m
e
tar
g
et
tr
ac
k
in
g
ap
p
licatio
n
s
f
o
r
g
im
b
al
s
y
s
tem
s
[
3
9
]
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
Sim
ula
t
io
n
re
s
ults
E
x
ten
s
iv
e
s
im
u
latio
n
s
wer
e
p
er
f
o
r
m
ed
u
tili
zin
g
th
e
Simscap
e
Mu
ltib
o
d
y
en
v
ir
o
n
m
en
t
in
MA
T
L
AB
/S
im
u
lin
k
to
v
er
if
y
th
e
ef
f
icien
c
y
o
f
th
e
co
m
b
i
n
ed
FAB
R
I
K
an
d
DE
ap
p
r
o
ac
h
.
T
h
e
in
tr
icate
3
D
C
AD
m
o
d
el
o
f
th
e
g
im
b
al
s
y
s
tem
was
im
p
o
r
ted
in
to
t
h
e
s
i
m
u
latio
n
p
latf
o
r
m
,
o
f
f
er
in
g
a
life
lik
e
an
d
p
r
ec
is
e
d
ep
ictio
n
o
f
th
e
s
y
s
tem
'
s
d
y
n
am
ics.
T
h
e
s
im
u
latio
n
s
ce
n
ar
io
s
en
co
m
p
ass
ed
d
iv
e
r
s
e
tar
g
et
tr
ajec
to
r
ies
an
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
to
ass
ess
th
e
alg
o
r
ith
m
'
s
p
er
f
o
r
m
an
ce
u
n
d
er
d
i
f
f
er
en
t
s
ettin
g
s
.
T
h
e
s
im
u
latio
n
s
r
ev
ea
led
th
at
th
e
in
teg
r
atio
n
o
f
t
h
e
alg
o
r
ith
m
s
u
b
s
tan
tially
e
n
h
an
ce
d
th
e
p
r
ec
is
io
n
an
d
s
p
ee
d
o
f
th
e
g
im
b
al
s
y
s
tem
'
s
tr
ac
k
in
g
ca
p
a
b
ilit
ies.
T
h
is
in
d
icate
s
a
h
ig
h
lev
el
o
f
p
r
ec
is
io
n
,
as sh
o
wn
in
Fig
u
r
e
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Mo
d
elin
g
a
n
d
en
h
a
n
ci
n
g
in
ve
r
s
e
kin
ema
tics
a
lg
o
r
ith
ms fo
r
r
ea
l
-
time
ta
r
g
et
…
(
A
b
d
era
h
m
a
n
K
r
io
u
ile
)
1551
Per
f
o
r
m
an
ce
m
ea
s
u
r
es,
in
clu
d
in
g
tr
ac
k
in
g
e
r
r
o
r
,
co
n
v
er
g
e
n
ce
tim
e,
an
d
r
o
b
u
s
tn
ess
to
d
is
tu
r
b
an
ce
s
,
wer
e
m
ea
s
u
r
ed
.
T
h
e
t
r
ac
k
in
g
er
r
o
r
,
wh
ic
h
is
m
ea
s
u
r
ed
as
th
e
E
u
clid
ea
n
d
is
tan
ce
b
etwe
en
th
e
lo
ca
tio
n
o
f
t
h
e
en
d
-
ef
f
ec
t
o
r
an
d
th
e
d
esire
d
p
o
s
itio
n
,
co
n
tin
u
o
u
s
ly
r
e
m
ain
ed
with
in
th
e
p
r
e
d
eter
m
in
ed
t
o
ler
an
ce
th
r
esh
o
l
d
.
T
h
is
g
r
ap
h
s
h
o
ws
th
e
tr
ac
k
i
n
g
er
r
o
r
o
v
e
r
tim
e
f
o
r
t
h
e
c
o
m
b
in
ed
FAB
R
I
K+
DE
alg
o
r
ith
m
co
m
p
ar
e
d
to
tr
ad
itio
n
al
m
eth
o
d
s
.
T
h
e
t
r
ac
k
in
g
er
r
o
r
is
d
ef
i
n
ed
as
th
e
E
u
c
lid
ea
n
d
is
tan
ce
b
etwe
en
t
h
e
e
n
d
-
ef
f
ec
t
o
r
p
o
s
itio
n
an
d
th
e
tar
g
et
p
o
s
itio
n
.
I
n
d
ee
d
,
th
e
tr
ac
k
i
n
g
er
r
o
r
o
v
er
tim
e
g
r
a
p
h
h
ig
h
lig
h
ts
th
e
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
o
f
th
e
co
m
b
in
ed
FAB
R
I
K+
DE
alg
o
r
ith
m
in
m
ain
tain
in
g
ac
c
u
r
ate
an
d
s
tab
le
tr
ac
k
in
g
.
T
h
e
lo
we
r
o
v
er
all
er
r
o
r
an
d
r
ed
u
ce
d
p
ea
k
er
r
o
r
s
s
ig
n
if
y
th
at
th
e
co
m
b
in
ed
alg
o
r
ith
m
p
r
o
v
id
es
a
m
o
r
e
r
eliab
le
s
o
lu
tio
n
f
o
r
r
ea
l
-
tim
e
tar
g
et
tr
ac
k
in
g
.
T
h
e
s
tab
ilit
y
an
d
c
o
n
s
is
ten
cy
in
tr
ac
k
in
g
er
r
o
r
ar
e
ess
en
tial
f
o
r
ap
p
licatio
n
s
wh
er
e
co
n
tin
u
o
u
s
an
d
p
r
ec
is
e
ad
ju
s
tm
en
ts
ar
e
r
e
q
u
ir
ed
.
T
h
e
co
m
b
i
n
ed
alg
o
r
ith
m
'
s
ab
ilit
y
to
q
u
ick
ly
c
o
r
r
ec
t
d
ev
iatio
n
s
en
s
u
r
es
th
at
th
e
g
im
b
al
s
y
s
tem
r
em
ain
s
o
n
tar
g
et,
ev
e
n
wh
en
s
u
b
jecte
d
to
d
y
n
a
m
ic
ch
an
g
es
in
th
e
en
v
ir
o
n
m
en
t
.
Fu
r
th
er
m
o
r
e
,
th
e
s
y
s
tem
d
e
m
o
n
s
tr
ated
a
h
ig
h
lev
el
o
f
r
esil
ien
ce
to
ex
ter
n
al
d
is
r
u
p
tio
n
s
,
co
n
s
is
ten
tly
m
ain
tain
in
g
a
s
tab
le
a
n
d
p
r
e
cise
tr
ac
k
in
g
ca
p
a
b
ilit
y
ev
en
wh
en
f
ac
e
d
with
u
n
f
o
r
esee
n
alter
atio
n
s
in
th
e
en
v
ir
o
n
m
en
t.
Fig
u
r
e
4
illu
s
tr
ates
th
e
d
is
tr
ib
u
tio
n
o
f
tr
ac
k
in
g
e
r
r
o
r
s
,
h
ig
h
lig
h
tin
g
th
at
th
e
c
o
m
b
in
e
d
FAB
R
I
K+
DE
alg
o
r
ith
m
co
n
s
i
s
ten
tly
o
u
tp
er
f
o
r
m
s
o
ld
e
r
ap
p
r
o
ac
h
es b
y
ac
h
iev
in
g
r
ed
u
ce
d
t
r
ac
k
in
g
e
r
r
o
r
s
.
Fig
u
r
e
3
.
T
r
ac
k
in
g
er
r
o
r
o
v
er
t
im
e
Fig
u
r
e
4
.
C
o
n
v
er
g
e
n
ce
tim
es f
o
r
d
if
f
e
r
en
t a
lg
o
r
ith
m
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
5
4
4
-
1
5
5
6
1552
T
h
e
tr
ac
k
in
g
er
r
o
r
d
is
tr
ib
u
tio
n
illu
s
tr
ated
in
Fig
u
r
e
4
em
p
h
asizes
th
e
ad
v
an
tag
es
o
f
th
e
co
m
b
in
e
d
FAB
R
I
K+
DE
alg
o
r
ith
m
o
v
er
tr
ad
itio
n
al
m
eth
o
d
s
.
T
h
e
n
a
r
r
o
w
an
d
c
o
n
ce
n
tr
ate
d
er
r
o
r
d
is
tr
ib
u
tio
n
ar
o
u
n
d
ze
r
o
m
eter
s
s
ig
n
if
ies
a
m
o
r
e
r
eliab
le
an
d
p
r
ec
is
e
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
,
wh
ich
is
cr
u
cial
f
o
r
h
ig
h
-
s
tak
es
ap
p
licatio
n
s
s
u
ch
as
s
u
r
v
eilla
n
ce
,
n
av
i
g
atio
n
,
a
n
d
s
cien
tific
o
b
s
er
v
atio
n
s
.
T
h
e
h
i
g
h
er
f
r
eq
u
en
cy
o
f
lo
w
e
r
r
o
r
s
d
em
o
n
s
tr
ates
th
at
th
e
FAB
R
I
K+
DE
alg
o
r
ith
m
p
r
o
v
id
e
s
co
n
s
is
ten
tly
ac
cu
r
ate
tr
ac
k
in
g
,
r
e
d
u
cin
g
th
e
lik
elih
o
o
d
o
f
s
ig
n
if
ican
t
d
ev
ia
tio
n
s
th
at
co
u
ld
c
o
m
p
r
o
m
is
e
t
h
e
g
im
b
al
s
y
s
tem
'
s
ef
f
ec
tiv
en
ess
.
T
h
is
r
o
b
u
s
tn
ess
in
m
ain
tain
in
g
lo
w
tr
ac
k
in
g
er
r
o
r
s
ev
en
u
n
d
er
v
ar
y
in
g
co
n
d
i
tio
n
s
f
u
r
th
er
u
n
d
er
s
co
r
es
th
e
p
r
ac
tical
b
en
ef
its
o
f
in
teg
r
atin
g
FAB
R
I
K
an
d
DE
alg
o
r
ith
m
s
.
T
h
e
p
er
f
o
r
m
a
n
c
e
in
th
e
p
r
esen
ce
o
f
d
is
tu
r
b
a
n
ce
s
,
as
s
h
o
wn
in
Fig
u
r
e
5
,
illu
s
tr
ates
th
e
r
esil
ien
ce
o
f
th
e
FAB
R
I
K+
DE
alg
o
r
ith
m
,
as
it
co
n
s
is
ten
tly
a
ch
iev
es
d
ec
r
ea
s
ed
tr
ac
k
in
g
er
r
o
r
s
ev
e
n
as th
e
d
is
tu
r
b
an
ce
le
v
els in
cr
ea
s
e.
T
h
ese
r
esu
lts
p
r
o
v
id
e
s
tr
o
n
g
e
v
id
en
ce
o
f
th
e
ad
v
a
n
tag
es
o
f
in
teg
r
atin
g
FAB
R
I
K
an
d
DE
a
lg
o
r
ith
m
s
f
o
r
g
im
b
al
s
y
s
tem
s
,
p
ar
ticu
lar
l
y
in
en
v
ir
o
n
m
e
n
ts
with
v
a
r
y
in
g
lev
els
o
f
d
is
tu
r
b
an
ce
s
.
T
h
e
c
o
m
b
in
ed
ap
p
r
o
ac
h
n
o
t
o
n
l
y
im
p
r
o
v
es
th
e
tr
ac
k
i
n
g
ac
cu
r
ac
y
b
u
t
also
en
s
u
r
e
s
th
at
th
e
s
y
s
tem
r
em
ain
s
r
e
s
ilien
t
to
ex
ter
n
al
p
er
tu
r
b
atio
n
s
.
T
h
is
m
ak
es
th
e
FAB
R
I
K+
DE
alg
o
r
ith
m
h
ig
h
ly
s
u
itab
le
f
o
r
ap
p
licatio
n
s
r
eq
u
ir
in
g
r
eliab
le
an
d
p
r
ec
is
e
tar
g
et
tr
ac
k
in
g
,
s
u
ch
a
s
in
s
u
r
v
eillan
ce
,
n
av
i
g
atio
n
,
an
d
s
cien
tific
o
b
s
er
v
atio
n
s
.
T
h
e
ab
ilit
y
to
h
a
n
d
le
d
is
tu
r
b
an
ce
s
ef
f
ec
tiv
el
y
wit
h
o
u
t
s
ig
n
if
ica
n
t
d
e
g
r
ad
atio
n
in
p
er
f
o
r
m
an
ce
u
n
d
er
s
c
o
r
es
th
e
p
r
ac
tical
ap
p
licab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
.
T
h
is
r
o
b
u
s
tn
ess
is
a
cr
itical
f
ac
to
r
f
o
r
th
e
d
e
p
lo
y
m
en
t
o
f
g
im
b
a
l
s
y
s
tem
s
in
d
y
n
am
ic
an
d
u
n
p
r
e
d
ictab
le
en
v
ir
o
n
m
en
ts
.
Fig
u
r
e
5
.
C
o
n
v
er
g
e
n
ce
tim
es f
o
r
d
if
f
e
r
en
t a
lg
o
r
ith
m
s
4
.
2
.
Rea
l
-
wo
rld v
a
lid
a
t
io
n
Fo
llo
win
g
th
e
s
u
cc
ess
f
u
l
s
im
u
latio
n
r
esu
lts
,
r
ea
l
-
wo
r
ld
e
x
p
er
im
en
ts
wer
e
co
n
d
u
cted
to
v
alid
ate
th
e
p
r
ac
tical
ap
p
licab
ilit
y
o
f
th
e
c
o
m
b
in
ed
al
g
o
r
ith
m
.
A
p
h
y
s
ica
l
p
r
o
to
ty
p
e
o
f
th
e
g
im
b
al
s
y
s
tem
was
co
n
s
tr
u
cted
b
ased
o
n
th
e
C
AD
m
o
d
el,
a
n
d
th
e
al
g
o
r
ith
m
was
im
p
lem
e
n
ted
o
n
an
em
b
e
d
d
ed
co
n
tr
o
l
p
latf
o
r
m
.
T
h
e
r
ea
l
-
wo
r
ld
test
s
in
v
o
lv
ed
tr
ac
k
in
g
m
o
v
in
g
tar
g
ets
u
n
d
er
v
ar
io
u
s
co
n
d
itio
n
s
,
in
clu
d
i
n
g
d
if
f
er
en
t
s
p
ee
d
s
,
tr
ajec
to
r
ies,
an
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
s
u
ch
as
win
d
an
d
v
ib
r
atio
n
s
.
T
h
e
ex
p
er
im
en
tal
r
esu
l
ts
clo
s
ely
m
atch
ed
th
e
s
im
u
latio
n
o
u
tco
m
es,
co
n
f
ir
m
in
g
th
e
alg
o
r
ith
m
'
s
ef
f
ec
tiv
en
ess
in
r
ea
l
-
wo
r
ld
s
ce
n
ar
io
s
.
T
h
e
g
im
b
al
s
y
s
tem
ac
h
iev
ed
h
i
g
h
tr
ac
k
in
g
ac
c
u
r
ac
y
,
with
m
in
im
al
d
e
v
iatio
n
s
f
r
o
m
th
e
tar
g
et
tr
ajec
to
r
y
.
T
h
e
s
y
s
tem
'
s
r
esp
o
n
s
iv
en
ess
an
d
r
o
b
u
s
tn
ess
to
d
is
tu
r
b
an
ce
s
wer
e
also
v
alid
ated
,
d
em
o
n
s
tr
atin
g
th
e
al
g
o
r
ith
m
'
s
ca
p
ab
ilit
y
to
ad
ap
t
to
d
y
n
am
ic
en
v
ir
o
n
m
en
ts
an
d
m
ain
tain
s
tab
le
tr
a
ck
in
g
p
er
f
o
r
m
an
ce
.
Fig
u
r
e
6
co
m
p
ar
es
th
e
ac
tu
al
tr
ac
k
in
g
p
at
h
v
s
.
th
e
tar
g
et
p
at
h
f
o
r
b
o
th
FAB
R
I
K+
DE
an
d
t
r
ad
itio
n
al
m
eth
o
d
s
.
T
h
e
co
m
p
ar
is
o
n
o
f
tr
ac
k
in
g
p
ath
s
s
h
o
wn
in
Fig
u
r
e
6
u
n
d
e
r
s
co
r
es
th
e
ad
v
an
tag
es
o
f
th
e
co
m
b
in
ed
FAB
R
I
K+
DE
alg
o
r
ith
m
in
m
a
in
tain
in
g
ac
c
u
r
ate
a
n
d
s
m
o
o
th
tr
ac
k
in
g
.
T
h
e
clo
s
e
a
d
h
er
e
n
ce
to
th
e
tar
g
et
p
ath
,
alo
n
g
with
r
ed
u
ce
d
la
g
an
d
o
v
er
s
h
o
o
t,
d
em
o
n
s
tr
ates
th
e
alg
o
r
ith
m
'
s
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
in
d
y
n
am
ic
en
v
ir
o
n
m
en
ts
.
Sm
o
o
th
a
n
d
p
r
ec
is
e
tr
ac
k
in
g
is
ess
en
tial
f
o
r
ap
p
licatio
n
s
s
u
ch
as
s
u
r
v
eilla
n
ce
,
n
a
v
ig
atio
n
,
an
d
s
cien
tific
o
b
s
er
v
atio
n
s
,
w
h
er
e
an
y
d
ev
iatio
n
f
r
o
m
t
h
e
tar
g
et
p
ath
ca
n
c
o
m
p
r
o
m
is
e
th
e
s
y
s
tem
'
s
ef
f
ec
tiv
en
ess
.
T
h
e
co
m
b
in
ed
alg
o
r
ith
m
'
s
ab
ilit
y
to
m
in
im
ize
th
ese
d
ev
iat
io
n
s
en
s
u
r
es
r
eliab
le
an
d
ac
cu
r
ate
tr
ac
k
in
g
o
v
e
r
ex
ten
d
ed
p
er
io
d
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
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&
C
o
m
p
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g
I
SS
N:
2088
-
8
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elin
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s
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tics
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ith
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1553
Fig
u
r
e
6
.
C
o
m
p
a
r
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o
n
o
f
tr
ac
k
in
g
p
ath
s
4
.
3
.
Co
m
pa
ra
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iv
e
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na
ly
s
is
A
co
m
p
ar
ativ
e
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aly
s
is
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o
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cte
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ate
t
h
e
p
e
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o
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m
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ce
o
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th
e
c
o
m
b
in
e
d
FA
B
R
I
K
an
d
DE
alg
o
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ith
m
in
co
m
p
ar
is
o
n
to
class
ic
in
v
er
s
e
k
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n
em
atics
m
eth
o
d
s
a
n
d
o
th
er
o
p
tim
izati
o
n
tech
n
iq
u
es.
T
h
e
m
etr
ics
u
tili
ze
d
f
o
r
co
m
p
ar
i
s
o
n
en
co
m
p
ass
ed
tr
ac
k
i
n
g
a
cc
u
r
ac
y
,
c
o
n
v
er
g
en
ce
tim
e,
an
d
co
m
p
u
tatio
n
al
ef
f
icien
cy
.
T
h
e
f
i
n
d
in
g
s
d
em
o
n
s
tr
ated
th
at
th
e
in
teg
r
ated
alg
o
r
ith
m
s
u
r
p
ass
ed
co
n
v
en
tio
n
al
tech
n
iq
u
es,
s
u
ch
as
g
eo
m
etr
ic
an
d
alg
eb
r
aic
m
eth
o
d
o
l
o
g
ies,
in
ter
m
s
o
f
p
r
ec
is
io
n
an
d
r
esil
ien
ce
.
T
h
e
DE
o
p
tim
izatio
n
im
p
r
o
v
e
d
p
er
f
o
r
m
an
ce
b
y
o
p
t
im
izin
g
th
e
jo
in
t
co
n
f
ig
u
r
atio
n
s
,
lead
in
g
to
r
ed
u
ce
d
tr
ac
k
in
g
er
r
o
r
s
an
d
s
h
o
r
ter
co
n
v
er
g
en
ce
tim
es.
T
ab
le
1
s
u
m
m
ar
izes
th
e
k
ey
p
er
f
o
r
m
an
ce
m
etr
ics
f
o
r
th
e
co
m
b
in
ed
FAB
R
I
K+
DE
alg
o
r
ith
m
,
t
r
ad
itio
n
al
m
et
h
o
d
s
,
GA,
an
d
PS
O.
T
h
e
m
etr
i
cs
in
clu
d
e
th
e
m
ea
n
tr
ac
k
in
g
er
r
o
r
an
d
m
ea
n
co
n
v
er
g
en
ce
tim
e.
T
h
e
p
er
f
o
r
m
an
ce
m
etr
ics
tab
le
h
ig
h
lig
h
ts
th
e
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
o
f
th
e
co
m
b
in
ed
FA
B
R
I
K+
DE
alg
o
r
ith
m
in
te
r
m
s
o
f
b
o
th
ac
c
u
r
ac
y
an
d
ef
f
icien
c
y
.
T
h
e
s
ig
n
if
ican
tly
lo
wer
m
ea
n
tr
ac
k
in
g
er
r
o
r
in
d
icate
s
th
at
th
e
co
m
b
i
n
ed
al
g
o
r
ith
m
p
r
o
v
id
es
h
ig
h
ly
p
r
ec
is
e
tr
ac
k
i
n
g
,
wh
ich
is
cr
u
cial
f
o
r
ap
p
licati
o
n
s
r
eq
u
ir
in
g
ex
ac
t
p
o
s
itio
n
in
g
a
n
d
co
n
tin
u
o
u
s
m
o
n
ito
r
in
g
.
T
h
e
f
av
o
r
a
b
le
m
ea
n
co
n
v
er
g
en
ce
tim
e
f
u
r
t
h
er
u
n
d
er
s
co
r
es
th
e
alg
o
r
ith
m
'
s
s
u
itab
ilit
y
f
o
r
r
ea
l
-
tim
e
ap
p
licatio
n
s
.
Qu
ick
co
n
v
er
g
e
n
ce
en
s
u
r
es
th
at
th
e
g
im
b
al
s
y
s
tem
ca
n
r
ap
id
ly
ad
j
u
s
t to
ch
an
g
es in
th
e
tar
g
et'
s
p
o
s
itio
n
,
m
ain
tain
in
g
ac
cu
r
ate
tr
ac
k
in
g
with
o
u
t d
e
lay
.
T
ab
le
1
.
Per
f
o
r
m
an
ce
m
etr
ics f
o
r
v
a
r
io
u
s
alg
o
r
ith
m
s
A
l
g
o
r
i
t
h
m
M
e
a
n
t
r
a
c
k
i
n
g
e
r
r
o
r
(
m)
M
e
a
n
c
o
n
v
e
r
g
e
n
c
e
t
i
m
e
(
s)
F
A
B
R
I
K
+
D
E
0
.
0
0
2
2
.
1
2
T
r
a
d
i
t
i
o
n
a
l
met
h
o
d
s
0
.
0
1
1
3
.
5
1
GA
0
.
0
7
5
3
.
2
2
PSO
0
.
0
6
5
2
.
8
1
4
.
4
.
Dis
cu
s
s
io
n
T
h
is
s
tu
d
y
h
ig
h
lig
h
ts
th
e
s
ig
n
if
ican
t
ad
v
an
tag
es
o
f
in
teg
r
atin
g
th
e
FAB
R
I
K
an
d
DE
alg
o
r
ith
m
s
f
o
r
r
ea
l
-
tim
e
tar
g
et
tr
ac
k
in
g
in
g
i
m
b
al
s
y
s
tem
s
,
a
cr
itical
co
m
p
o
n
en
t
in
m
o
d
e
r
n
ap
p
licatio
n
s
s
u
ch
as
s
u
r
v
eillan
ce
,
ae
r
o
s
p
ac
e,
an
d
r
o
b
o
tics
.
B
y
lev
er
ag
in
g
th
e
co
m
p
u
tatio
n
al
ef
f
icien
cy
o
f
FAB
R
I
K
an
d
th
e
r
o
b
u
s
t
o
p
tim
izatio
n
ca
p
ab
ilit
ies
o
f
DE
,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
ac
h
iev
es
a
b
ala
n
ce
d
s
o
lu
tio
n
th
at
ex
ce
ls
in
b
o
th
ac
cu
r
ac
y
an
d
r
esp
o
n
s
iv
en
ess
.
T
h
e
in
teg
r
ate
d
ap
p
r
o
ac
h
n
o
t
o
n
ly
s
tr
ea
m
lin
es
th
e
co
m
p
u
tatio
n
al
p
r
o
ce
s
s
es
b
u
t
also
en
s
u
r
es
r
eliab
le
p
er
f
o
r
m
a
n
ce
in
d
y
n
a
m
ic
an
d
ch
allen
g
in
g
e
n
v
ir
o
n
m
en
ts
.
Valid
atio
n
th
r
o
u
g
h
e
x
ten
s
iv
e
s
im
u
latio
n
s
an
d
r
ea
l
-
wo
r
ld
e
x
p
er
im
e
n
ts
h
as
r
ein
f
o
r
ce
d
th
ese
f
in
d
in
g
s
,
d
em
o
n
s
tr
atin
g
th
e
m
et
h
o
d
'
s
ab
ilit
y
to
ad
ap
t
to
ch
an
g
in
g
co
n
d
itio
n
s
an
d
ex
te
r
n
al
d
is
tu
r
b
an
ce
s
.
T
h
is
ad
ap
ta
b
ilit
y
is
p
ar
ticu
lar
ly
im
p
o
r
tan
t
i
n
s
ce
n
ar
io
s
wh
er
e
s
tab
ilit
y
an
d
p
r
ec
is
io
n
ar
e
ess
en
tial,
s
u
ch
as
in
tr
ac
k
in
g
m
o
v
in
g
tar
g
ets
o
r
s
tab
ilizin
g
im
ag
in
g
s
y
s
tem
s
u
n
d
er
m
o
tio
n
.
A
k
ey
s
tr
en
g
th
o
f
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
lies
in
th
e
iter
ativ
e
n
atu
r
e
o
f
th
e
D
E
alg
o
r
ith
m
,
wh
ich
co
n
tin
u
o
u
s
ly
r
ef
in
es
jo
in
t
c
o
n
f
ig
u
r
atio
n
s
,
en
s
u
r
in
g
th
e
s
y
s
tem
'
s
o
p
tim
al
p
er
f
o
r
m
an
ce
u
n
d
er
d
y
n
a
m
ic
co
n
d
itio
n
s
.
T
h
is
ca
p
ab
ilit
y
allo
ws
th
e
m
eth
o
d
to
ef
f
ec
tiv
ely
h
an
d
le
r
ea
l
-
tim
e
o
p
er
atio
n
al
ch
allen
g
es
,
Evaluation Warning : The document was created with Spire.PDF for Python.